Kishore Dutta (Handique Girls' College Guwahati, India): Evolving networks for realization of cultural evolution.
Dynamical processes that took place over different spatial and temporal scales throughout the evolutionary pathway of human civilizations. How the different socio-physical processes such as diffusion, migration, assimilation, aggression, and annihilation drive the evolutionary pathway of human culture from its prehistoric nascent form to the modern hierarchically complex multicultural one remains one of the challenging problems of potential implications that essentially demands interdisciplinary research. Questions arise as to why most of the cultures go extinct and why some survive for a comparatively longer period even after facing several wars and attacks. What interactions or rules play a key role in shaping the monocultural-to-multicultural phase transition? In order to carry out a detailed quantitative investigation on such problems, in this project, we shall employ the evolutionary algorithms and evolving networks as statistical tools for dynamical evolution of human cultures and discern how different dynamical processes acting at different spatial scales affect the emerging behavior of the social networks. This would allow us to identify the key processes involved in determining the emergent large-scale and long-term patterns and trends of cultural evolution, as documented by anthropologists, archaeologists, historians, and linguists. It would also open up new avenues for investigating how complex social structures remain prone to external perturbations caused by the invasion or the emergence of deadly epidemics
Gabriel Marghoti (Departamento de Física da Universidade Federal do Paraná, Brazil): Beat Frequency Induced Transitions in Synchronization Dynamics.
In neurosciences, the brain processes information via the firing patterns of connected neurons operating across a spectrum of frequencies. To better understand the effects of these frequencies in the neuron dynamics, we have simulated a neuronal network of Izhikevich neurons to examine the interaction between frequency allocation and intermittent phase synchronization dynamics. As the synchronized population of neurons passes through a bifurcation, an additional frequency mode emerges, enabling a match in the mean frequency while retaining distinct most probable frequencies among neurons. Subsequently, the network intermittently transits between two patterns, one partially synchronized and the other unsynchronized. Through our analysis, we demonstrate that the frequency changes on the network lead to characteristic transition times between synchronization states. Moreover, these transitions adhere to beat frequency statistics when the neurons frequencies differ by multiples of a frequency gap. Finally, our results can improve the performance in predicting transitions on problems where the beat frequency strongly influences the dynamics.
Pablo Padilla (Institute for Applied Mathematics, UNAM, Mexico): Understanding musical style with complex networks.
We present work aiming to provide an analytic characterisation of musical style and its evolution (see https://formal-methods-in-musicology.webnode.page/introduction/). We construct melodic, harmonic and rhythmic transition matrices that determine a graph. We then study the properties of the associated networks.
Dario Agudelo (Universidad Autónoma de Manizales, Colombia): Analysis of dynamic networks based on the Ising model for the case of study of co-authorship of scientific articles.
Two computational methods based on the Ising model were implemented for studying temporal dynamic in co-authorship networks: an interpretative for real networks and another for simulation via Monte Carlo. The objective of simulation networks is to evaluate if the Ising model describes in similar way the dynamic of the network and of the magnetic system, so that it can be found a generalized explanation to the behaviours observed in real networks. The scientific papers used for building the real networks were acquired from WoS core collection. The variables for each record took into account bibliographic references. The search equation for each network considered specific topics trying to obtain an advanced temporal evolution in terms of the addition of new nodes; that means 3 steps, a time to reach the interest of the scientific community, a gradual increase until reaching a peak and finally, a decreasing trend by losing of novelty. It is possible to conclude that both methods are consistent with each other, showing that the Ising model can predict behaviours such as the number and size of communities (or domains) according to the temporal distribution of new nodes.
Bruno Rafael Reichert Boaretto (Universidade Federal de São Paulo, Brazil): Emergence of Phase Synchronization in Sparse Neuronal Networks under Poissonian Spike Inputs.
This study explores the phenomenon of phase synchronization within sparse neuronal networks, focusing on the interplay of dynamics under the influence of Poissonian spike inputs. Utilizing the Hodgkin-Huxley model to simulate neuronal behavior, we observe the emergence of irregular spiking patterns within specific ranges of conductances. Notably, our investigation reveals that phase synchronization among neurons occurs when external stimulation induces spiking activity without surpassing the coupling threshold. Conversely, excessively high external currents lead to desynchronization within the network. We elucidate these phenomena by considering various mechanisms, including incoherence, current minimization, and stochastic effects arising from Poissonian inputs. Furthermore, our numerical simulations demonstrate intriguing scenarios where selective neuronal stimulation induces synchronization in non-stimulated regions of the network, as well as the propagation of spiking activity under increased coupling conditions.
Fernando da Silva Borges (State University of New York (SUNY), USA): Self-sustained activity and intermittent synchronization in balanced networks.
Self-sustained activity in the brain is observed in the absence of external stimuli and contributes to signal propagation and cognitive processes. In this work, using intracellular recordings from CA1 neurons and networks of adaptive exponential integrate-and-fire neurons (AdEx), we demonstrate that self-sustained activity presents high variability of patterns with low neural firing rates and small-bursts in distinct neurons. We show that both connection probability and network size are fundamental properties that give rise to self-sustained activity in qualitative agreement with our experimental results [1]. Moreover, we provide a more detailed description of self-sustained activity in terms of lifetime distributions, synaptic conductances, and synaptic currents. After this, we considered synaptic modifications that can be related to activity-regulated cytoskeleton-associated (ARC) protein. Particularly, we included connectivity alterations in intense ARC immunoreactive neurons (IAINs) observed in the rodent epileptic model [2]. We observed that these alterations contributed to the appearance of epileptic seizure activity and intermittent up and down activities associated with synchronous bursts and asynchronous spikes, respectively. We characterized the intermittent activity and applied the optogenetics control. Synchronized burst patterns are controlled when IAINs are chosen as photosensitive, but not effective in non-IAINs, showing that IAINs play a pivotal role in both the generation and suppression of highly synchronized activities.
[1]. Borges FS, Protachevicz PR, Pena RFO, et al. Self-sustained activity of low firing rate in balanced networks. Phys A, 2020, 537, 122671.
[2]. Borges FS, Gabrick EC, Protachevicz PR, et al. Intermittency properties in a temporal lobe epilepsy model. Epilepsy & Behavior, 2023, 139, 109072.
Juliane Teixeira de Moraes (Universidade Federal de Viçosa, Brasil): Visibility graphs for non-equilibrium phase transitions.
The Visibility Graph (VG) is a tool to map time series into graphs. This method has attracted attention recently because of its practical and simple implementation. Since most dynamic systems can be expressed through time-ordered data, it is relevant to look for new time series analysis techniques. The VG showed as a modern method in this sense because instead of analyzing the time series itself, one can use the huge toolbox of complex network measures and study the generated graph. Thus, given a time series, two values are connected in the corresponding graph if they present visibility between them, following a geometric criterion. The dynamical system we choose to investigate is a spreading process taking place in a network structure. Many important problems can be related to this system such as the propagation of an infectious disease in a population or the dissemination of rumors and information as well. Therefore, we are interested in understanding how the spreading phenomena occur in different structures by looking at the time series of the density of infected individuals. We tackle this issue mainly from the theoretical point of view. It is known that the Contact Process model performs an absorbing state phase transition in different network structures. Using a measure called degree correlations of the VG we were able to distinguish between time series that belong to critical and off-critical regimes in this model. Also, we investigated the differences between a continuous and a discontinuous phase transition using a variation of the model. Our perspectives include investigating if the VG could provide information on the original network structure in which the spreading phenomenon is happening. In general, the unique information available in a dissemination process is a time series of infected individuals. Therefore, taking information from it on the whole phenomenon and the nature of the connections between the individuals is a challenging task that could be handled by the method proposed in this work. Acknowledgments: Authors thank the financial support of CAPES, FAPEMIG, and CNPq.
Federico Sevlever (INEU - Fleni - CONICET, Argentina): Defining Network Topologies that Can Achieve Molecular Memory.
In the context of cellular signaling and gene regulatory networks, the concept of molecular memory emerges as a crucial determinant of molecular mechanisms. This study introduces a novel memory quantifier designed to comprehensively capture and quantify the memory of a system in response to transient stimuli. We proposed and validate this quantifier through toy models, showcasing its effectiveness in systems with positive feedback loops and bistability. In addition, we develop an algorithm to assess long-term memory in circuits, leading to the identification of minimal motifs that play pivotal roles in conferring memory. The research explores the comparative impact of positive and negative feedback loops on memory, revealing that positive feedback enhances memory while certain negative feedbacks may diminish it. An intriguing finding emerges as oscillating circuits, even in the absence of positive feedback, exhibit memory, with the phase of oscillations storing information about stimulus duration. Finally, we experimentally validate the quantifier using mouse Embryonic Stem Cells (mESCs) subjected to transient differentiation stimuli. The proposed memory quantifier is applied to gene expression dynamics, revealing varying degrees of memory retention among different genes. The vectorial nature of the quantifier proves advantageous in capturing the holistic memory dynamics of the system.
Matheus Palmero (Institute of Physics, University of Sao Paulo (IFUSP), Brazil): Recurrent Chaotic Trajectories in a Time-Dependent Potential Well Model.
In this study, we show that recurrence analysis of chaotic trajectories provides useful knowledge of their dynamical behaviour. By defining an ensemble of initial conditions, evolving them until a given maximum iteration time, and computing the recurrence rate of each orbit, it is possible to find particular trajectories that widely differ from the average behaviour. Based on this approach, we analyze the effects of these recurrent chaotic orbits in a symplectic model for a time-dependent potential well. We show that for specific values of parameters and initial conditions, the system may experience transitory states of high energy caused by temporary but sufficiently long quasi-periodic dynamics in chaotic regions of the system's phase space.
Emanuel Fortes Teixeira (UFRGS, Brazil): A single active ring model with velocity self-alignment
Cellular tissue behavior is a multiscale problem. At the cell level, out of equilibrium, biochemical reactions drive physical cell–cell interactions in a typical active matter process. Cell modeling computer simulations are a robust tool to explore countless possibilities and test hypotheses. Here, we introduce a two-dimensional, extended active matter model for biological cells. A ring of interconnected self-propelled particles represents the cell. Neighboring particles are subject to harmonic and bending potentials. Within a characteristic time, each particle's self-velocity tends to align with its scattering velocity after an interaction. Translational modes, rotational modes, and mixtures of these appear as collective states. Using analytical results derived from active Brownian particles, we identify effective characteristic time scales for ballistic and diffusive movements. Finite-size scale investigation shows that the ring diffusion increases linearly with its size when in collective movement. A study on the ring shape reveals that all collective states are present even when bending forces are weak. In that case, when in a translational mode, the collective velocity aligns with the largest ring's direction in a spontaneous polarization emergence.
Leonardo dos Santos Ferreira (UFRGS, Brazil): A random matrix model for the stability of heterogeneous Ornstein-Uhlenbeck processes on top of highly connected networks.
We study a class of multivariate Ornstein-Uhlenbecck processes, characterised by the reversibility condition and by heterogeneous temperatures. Benefiting from a complex network description, we associate each stochastic process to the node of a homogeneous network, where each dynamical variable performs a macroscopic number of connections. The microscopic state variables evolve according to a Langevin equation, with a linear field generated from the interaction between neighbours and the stochastic heterogeneous noise introduced by temperature. We propose a random matrix ensemble for the connection matrix that yields a microscopic intepretation of the correlations originated from the linear interactions and the heterogeneous temperatures in the system. We find that, in the presence of heterogeneous temperatures, the spectral properties of the stationary correlation matrix can be used to describe the phenomelogy of the original dynamical system, generalizing a myriad of previous works that established a stability theory for the time series in the absence of temperature, based on the eigenspectrum of the coupling matrix.
Guilherme Costa (ICTP-SAIFR/IFT-UNESP, Brazil): The influence of external drives on the frustrated Kuramoto model.
The emergence of synchronization and its general features are of particular interest to scientists working on several subjects, such as physics, social sciences and biology. From neurons to population dynamics and fireflies, nature showcases several examples of synchronized and collective behavior. The paradigmatic model to investigate synchronization phenomena was proposed by Kuramoto in 1975, in which oscillators are coupled by a scalar k. In the past years, several models with more complex couplings have been proposed and studied, such as higher order or matricial interactions. The introduction of matrix coupling may break the rotational symmetry of the system, leading to novel synchronized states. However, in some systems, synchronization is dependable on external stimuli, such as information pro- cessing on the brain, that may be triggered by sensorial inputs. In addition, most of those external drives acts only on a fraction of the system. Thus, the wide variety of phenomena involving synchronization under partial or global stimuli motivates the study of mathematical models that describes those systems. In this way, we in- vestigated the generalized frustrated Kuramoto model under the action of external drives acting integrally and partially on the system both using analytical and nu- merical methods. The major finding of this investigation was the existence of bands of synchronization known as Arnold tongues, i.e., broad regions of phase locking between the periodic drive and the natural frequency of the oscillators, that does not occur on the original Kuramoto model under the same conditions. Additional simulations considering real and synthetic networks were performed to backup the findings. We acknowledge the financial support of FAPESP (grant 2023/03917-4), CNPq and CAPES.
Thomas Peron (Institute of Mathematics and Computer Science/USP, Brazil): Synchronization in high dimensions: mean-field theory of vector spin models on networks with arbitrary degree distributions.
Understanding the relationship between the heterogeneous structure of complex networks and cooperative phenomena occurring on them remains a key problem in network science. Mean-field theories of spin models on networks constitute a fundamental tool to tackle this problem and a cornerstone of statistical physics, with an impressive number of applications in condensed matter, biology, and computer science. In this work we derive the mean-field equations for the equilibrium behavior of vector spin models on high-connectivity random networks with an arbitrary degree distribution and with randomly weighted links. We demonstrate that the high-connectivity limit of spin models on networks is not universal in that it depends on the full degree distribution. Such non-universal behavior is akin to a remarkable mechanism that leads to the breakdown of the central limit theorem when applied to the distribution of effective local fields. Traditional mean-field theories on fully-connected models, such as the Curie--Weiss, the Kuramoto, and the Sherrington–Kirkpatrick model, are only valid if the network degree distribution is highly concentrated around its mean degree. We obtain a series of results that highlight the importance of degree fluctuations to the phase diagram of mean-field spin models by focusing on the Kuramoto model of synchronization and on the Sherrington--Kirkpatrick model of spin-glasses. Our results put forward a novel class of spin models that incorporate the effects of degree fluctuations and, at the same time, are amenable to exact analytic solutions.
Paulo Cesar Ventura (Indiana University, USA): Combining within and between-host epidemic dynamics in a multiplex synthetic population.
Within-host viral dynamics models are effective tools for estimating epidemiological parameters like the generation time (the interval between consecutive infections) and the pre-symptomatic transmission rate (the proportion of infections occurring before symptom onset). However, the clustered nature of human contacts introduces biases unaccounted by within-host dynamics models. To quantify these biases realistically, we developed a multiscale model integrating within-host viral dynamics and between-host transmission, using the ancestral lineage of SARS-CoV-2 as a case study. The within-host component employs ordinary differential equations to simulate viral replication, calibrated with empirical viral load data from 210 SARS-CoV-2-infected individuals. The between-host component uses a data-driven multiplex network model, incorporating four layers of human contacts: households, workplaces, schools, and the community. The within-host dynamics drives the infectiousness in the between-host component. Our findings reveal significant biases due to network clustering effects. For a basic reproduction number (R₀) of 3, our model demonstrates a 13% disparity in the generation time compared to estimates from within-host dynamics only, and an 8% deviation in the pre-symptomatic transmission rate. Moreover, when compared with a between-host-only transmission model, our multiscale model yields similar macroscopic outcomes (e.g., incidence and reproduction number trajectories) but diverges notably in how the generation time and pre-symptomatic transmission rate change with R₀. This underscores the importance of accounting for both within-host viral dynamics and the clustered structure of between-host contacts for accurately estimating epidemiological metrics. Furthermore, our multiscale modeling approach enables estimation of quantities that are rather challenging to measure through field investigations.
Rodrigo Malavazi Corder (University of Sao Paulo, Brazil): The spark of synchronization in heterogeneous networks of chaotic maps.
We investigate the emergence of synchronization in heterogeneous networks of chaotic maps. Our findings reveal that a small cluster of highly connected maps is responsible for triggering the spark of synchronization. After the spark, the synchronized cluster grows in size and progressively moves to less connected maps, eventually reaching a cluster that may remain synchronized over time. We explore how the shape of the network degree distribution affects the onset of synchronization and derive an expression based on the network construction that determines the expected time for a network to synchronize. Understanding how the network design affects the spark of synchronization is particularly important for the control and design of more robust systems that require some level of coherence between a subset of units for better functioning. Numerical simulations in finite-sized networks are consistent with this analysis.
Rodrigo da Motta (Federal University ABC, Brazil): A Novel Method to Investigate Neurodevelopment Using Ising Temperature and Graph Neural Networks.
One of the biggest challenges in neuroscience is comprehending brain function mechanisms on different temporal and spatial scales. In particular, the topic of neurophysiology during the resting state at the macroscopic level is of great interest, not only in contribution to neurodevelopment and psychiatry but also to emergent patterns that microscopic components cannot explain. Recent studies show that brain dynamics may be modelled by lattice models near criticality, such as the 2D Ising Model. The Ising temperature, which is the order parameter dictating the phase transitions of the model, is being used to better understand different brain states. This work aims to investigate neurodevelopment through a novel method to estimate the Ising Temperature of the brain from functional Magnetic Resonance Imaging (fMRI) data using functional connectivity and Graph Neural Networks (GNNs) trained with Ising Model networks.
Rodrigo da Motta (UNICAMP, Brazil): Active and chaotic swarmalators.
Several systems in nature show the emergence of synchronization and swarming of their constituent individuals. Both phenomena, occurring respectively in time and space, have been studied using independent frameworks such as the Kuramoto and the Vicsek models. In this talk, we present the swarmalators model, which characterizes systems of particles able to swarm and synchronize while also allowing the interplay of both phenomena. We focus on instances of this model that define Kuramoto-like interactions between individuals to facilitate the analytical study of their emergent states. Despite the simplifications, these models allow for the arising of active patterns, some coherent with the original states and some new, reminiscent of vortex-like structures. Finally, within the active regime, we also show the emergence of chaos.